CA2276971A1 - Preamble using golay sequence for access channel in cellular communications systems - Google Patents

Abstract

A preamble for a reverse access channel (RACH) of a CDMA (code division multiple access) communications system comprises a pair of constituent Golay sequences A and B concatenated at least one pair, and preferably a plurality of different pairs, of transformed sequences which are also constituent Golay sequences, each pair of transformed sequences comprising a permutation of elements of the pair of sequences A
and B. The permutations can include a reversed order of elements in the sequences, a reversed order of some or all of a set of address bits identifying locations of elements in the sequences, a concatenation of subsets of elements in odd and even locations of the sequences A and B, and combinations of these permutations. A method for providing the preamble, and related apparatus using a bidirectional counter (30) and an address permutation unit (32), are described.

Description

JUL !.~ 'y'J 15~4 rK HI h'I-IItNIS b13 'f~l .3101'f IU b 1 tilt 'j'3 ~4'fb h'.ID4/dj pREAME1.,B USING GOLAY SEQU~GE FOR ACGBSS CHANNEL
rhT CELLULAR COIvIMUNICA'~4NS SYSTEMS
'This iaveation relates to preambles using a Golay sequence for afl access channel.
in particular a so-called reverse access channel (RACH). in a cellular communications system..
und~f ~Ia~Gll~
In celiular comrnuctixadons systems, for example in a wireless celluiar commuaicaaons system using CDMA (code division multiple access) teclxuiques for communications between a mobile terminal or station (MS) and a bass station (BS), it is lO well known far the BS to transmit a pilot signal and a broadcast nnessage including a psneamblc. On being powered up in a cell associated with the BS, a MS uses the pilot signal for synchronization to thv BS, and downloads ixtfornaation including the pteannble from the broadcast message. Laving accordingly detertnaned tlx timing of the BS. the MS transmits the preamble on the RACH. This is detected by the BS using eornlation teelmigues, so that the BS is informed of the MS, and it can proceed with establishing co~ications on a traflqc chanwel between the BS and the MS.
In submission TSGR1~3(99)203 to the'1'SG-RAN Worklag Croup 1 meting X13, March 22-26,1999, entitled "New RACK preambles with low aut~o-carrelatio~n sidelobea and reduced detector coanplcaity" (a copy of which is included herein as an Appendix at 24 the end of the description), it is proposed that the prcanuble, which comprises 4~p96 code chips providing one of 16 orthogonal signatunas of length 1$ complex sigasls, be provided by binary Golay sequences, which have the advantageous property that the suxn of choir aperiodic auto-correlation functions is zao for all non-zero time shifts.
Consequently, that submission.prdposes that the preamble be formed from a pair of wmplementary sequences A end B, which together constitute a Golay sequence and are refezred to as constituent Golay sequences, each of 256 chips, repeated in a specific one of 16 signatum patterns. so that the overall sequence has a length of 4096 chips, as shown by Table I below.
In Table 1, the signature pa~enas include the sulueaces A sad B in normal and 34 inverted forms, the inverted forms being denoted -A and -B respxtively. The 4096 chiQa of an overall sequence can co~nvcniont7y be included in one 10 nas time slot, the aa~astituent Golay sequences A and H being individual to a specific cell andlor BS, and the above signature patterlns being the same far all cells and base stations.
In contzast to using longer distiuoctive codes or sequences each of 4096 chips to identii"y the BS and any of 16 ustrs, far which matched Elter3ng would be rtquired for sequences of 4096 chips, this preamble con~structioa enables the matched filtering to be applied to the much shorter sequences of 256 chips, with a consequent substantial Induction iua computational coxnplaxity.

r J UL 19b "j'-J 15 ~'~'4 I-K N I h'H I tN I 5 61,5 'f~l .i101'f I U b 1 iil J
J5,5 ~4'fb h'. b5~~i 1 A A B B A -A .-BB A -A B -B A A -B -B

4 A A B -B A A -B -B --A,A -B -H -A A B -B

A A H B -A A B -B A -A B -B A A B B

6 A A. B B -A A B -B -A A -B B A A -B -B

A A -B -1~A A B -B -A A B -B A -A -B -H

12 A A -H B A, A B B A A B B A A -B B

13 A A -8 -B A A -B $ A A -B B A A -B -B

14 A A -B -H -A A -B B A A B -B A A, B B

A, -A -B . A A -B -B A A -B B -A A -B B
B

lb A A -B B -A A -B -B A A B B A A B -B

Table ft has been found, however, that C~olay sequences (and Gold code sequences which have previously been proposed) Produce substantial cross correlation peaks for 5 time shifts corresponding to 256 chip boundaries, corresponding for example to a communication distanca of about 9 Icm. Such uz>Idesired cross correlation peaks are und~taod to be due to the xepetidvc nature of the constituent sequences in the signature patt«ns discussed above, and preacnt a significant ck~allenge if the dalay due to communications distance can correspond to the preamble length or a multiple of the 10 preamble length, and hence for situations where it is desired to use a relatively short preamble and relatively large cell sizes.
Accordingly, aspects of this inventiaa seek to provide an improved pmaanble, and ~thod for providing such a preamble, for use in an access channel of a communications system, a method of producing an emended sequence frrnm a pair of constituewt Golay 15 sequez>toes, and related apparatus.
Summa~"pf rpn one aspect of this invention provides a method of producing an extended sequence fropn a pair of constituent Golay sequences A and B, comprising the steps of:
transforming the pair of constituent C3olay sequences A and B to form at least one pair of transformed sequences which are also constituent Ciolay sequences; and concatenating at least two of said pairs of constituent ~iolay sequences to produce the extended sequ~ncc.

The step of transforming the pair of constituent t3olay seqrrenccs A and H oo form each pair of transfanm~ed sequences gt~aably eompxis8s a permutation of elements of tlae sequences. The permutation can eomprisa, for example, a reversal of the order of elements in the scqWSirccs, a reversal of a sot of addr~esa bits identifying locations of elements in the sequences. a reversal of some but not all of a set of address bits identifying locations of elements a~n the seduencea, or a concatenation of subsets of ele~aents of the sequences selected by decimatiozr, for example a concatenatiarr of two subsets of elements, in coon and odd locations in the sequences, or it can comprise combinations of these permutations.
Tire invention also provides a method of producing a preamble for use on an acesas eliannel of a cxllular commwnicatlons system, wherein the preamble includes as extended sequence produced by the above method. Ia particular, each of the constituent Ciolay aequeaces A and B and each of the transformed sequences can cormpriae elocnemts, and the preamble can eomprisd 4096 elements. Advusly in this case the 1 ~ extended sequence caa comprise the constituent C3olay soquaixs A and B and seven different transformations of these sequences A and H.
Another aspect of this tllyention provides a method of pravidiag a gamble for an aaoess channel of a GDMA (code division rnvltiplo access) commuaications system, coxuprising the steps of providing a pear of constituent (3olay sequences A
and B;
permuting elf of the pair of sequences A and B to form at least one pair of transformed sequences which are also constituent Oolay sequences; and eoncatenaEiag said at least one pair of tranafortncd sequences with the pair of constituent Golay sequences A and B for use as an extended sequence in the preamble.
The preamble can be provided by a eoneate~natio~n of the pair of constituent Golay sequences A and B with a plurality of pairs of said transforured sequences acxording to different permutations of ttro clernents of the pair of constituent Cl"olay sequences A and s.
The step of permuting elennents of the pair of sequences A and B can comprise a reversal of the order of elements in tha seguoncea, a reversal of at least some of a set of address bits identifying locations of elements in the sequences, or a concatenation of two subsets 3U of elements of the sequences, the two subsets corxtrsponding rsapactively to even acrd odd locations in the sequences.
The invention further provides apparatus for use in carrying out the above tnethoda, couaprising a aroxrrory for scaa~ing elements of e~h sequence, and addrtas control mans for addressing the memory for writing to or reading fro~acr the memory 3~ consecutively at locations according to the transformed sequences. The address control means can oompiise a bidirxtional counter for supplying memory addresses increnneated in either of two opposite dirccxians, and an address permutation unit far permutiurg said Jt~. 49b '~J 1~~~ fK NI h'HItNlS 613 'f~l 3b1'f IlJ b 1 al's ~3 ~4'rb h'.1?fi~i addresses in accordatu'.e with flee cransfatmed sequences and for supplying the permuted addresses to the memory.
'rat another aspect of the invention provides a preamble far an aaoess channel of a CDMA (code division multiple axess) communications system, comprising a pair of constituent Oolay sequester A and B sitd. concatenated with the pair of oonstituem Ciolay sequences A and B, at least one pair of transformed saquencos which are also oonstitueat Galay sequences. each pair of transformed sequeaves comprising a permutation of alam~ts of the pair of seguencos A sad B.
The preamble can compriso a plurality of pairs of said transfau~d sEqueaces having diPPcrent respective permutations of. the elcrnarts of the pair of sequences A and B.
In particular, r~espect3ve pair of transformed sequences eaa comprise the pair of sequences A and B with a reversed order of elements in the Sequences, the pair of sequences A and B with elements in the seduences permuted is accordance with a reversed order of at last same of a set of address bats identifying locations of elements inn the sequences, and alerncnta in odd locations of the pair of sequences A and B
concatenated with elamrnta in even locations in the pair of sequences A Bad B.
)brief Dascriptio~f sIIO.I?d~C1'~
The iunvention wilt be fiutber understood from the following description with reference to the accompanying drawings. iii which:
24 Figs. l to 4 are diagrams illustrating various transformations any of which may be carried out in icnplornentations of the iaventian;
Fig. 5 schematically illustrates in s block diagraux stages of a C3olay sequence generator lanown in the art;
Fig. 6 schematically illustrates in a block diagram stages of a Clolay sequence rarrelstar known in the err; and Fig. 7 schem,aticahy illustrakas in a block disgr~n a preamble correlator and signatum detector according to as embodiment of tlx invention.
Detailrin~
Embodiments of this inventio~a serve to perform various uangforms, alone or izi 3A combunacions, on the constituent Golsy sequences that ate used to provide a concatenatod preamble and signature. ~ a manner that can eliminate or substantially reduve the undesired cross eorralatlon peaks discussed above. Soma of tlxae transforms era referred to as sequezree reversal, address bit reversal; partial bit reveal, sad resampling or even-odd gartiuo~ng, ~d $n ~scu~ssed is f~uther detail below. Tht invention is also applicable to other transforms, and combinations of these and other transForms, tb~at provide similar results grad that may occur to tt~se of ordinary skill in the art andlor are discussed later below. Zn each cast the transform is applied to the two constituent Oolay JUL Idb ' J~ 15: ~ hK N I h'H I tN 15 bl,i 'f~l .3b1'f I U b 1 lily y5,5 ~4'fb h'. ~~i sequences A and B to rasult in another two sequences which, it can be shown, are also Golay sequences.
This trauafos<m revessos the oadez of all of the elements of the coaistitu~t t3olay 5 saluences A and H to produce new constituent t3olay seguenoES A* and B*
respeetively_ Thus if the seguene~ A and B are gives by:
A = ~ al, a2, ... aN_i. aN ~ B = ~ bl, b~, . . _ bN_l. bTT
then tho sequences A* and B* am given by:
A* . ~ aN, aprl.... a2, al ~; B* ~ ~ bN. bN_1, ... b2, bi 'rite preamble a~ad signature cacrl then be fornadd from both the two eansatc~nlt Ciolay sequences A and B and the two reversed seduencas A* and B*, is each case witkt ~T = 256 chips, as shown by the following Table 2, in which the 16 signature patterns, represented by'the normal sad inverted (-) forms of the sequences, are the same as in the followiung Table 2:

1 A B A* B* A B -A*B* A -B A* -B* A B -A*-B*

2 A B A* B* A -B -A*B* A B A* B* A -B A'sB*

3 A -B A* -H* A B -A*-B*A B A* B* A B -A*B*

4 A -B A* B* A B -A*-B*A -B -A*-B* A B A* -B*

5 A B A* B* A B A* -B*A -B A* -B* A -B A* B*

6 A B A* B* A B A* -$'~-A B -A*B* A $ -A*-S*

7 ,A -B A* B* A -B A* B* A B A* $* A B A* -B*

8 A B A* -B* -A _g A* B* -p ~ A* -$* A -B -A*B*
. -B

9 A B -A*-B* A -B A* -B*A -B -A*B* A B A* B*

10 A B -A*-B* A -B A* -B*A B A" _B* -A,g _A*-Hw 11 A -B A* B* A B A* B* A B -A*-$* A -B A* -B*

1z A -B A* B* A B ~ B* A -B A* B* A. B -A*B*
A*

13 A B -A*-B* _p B -A*B* ~, -B -A*B* ,~._g -A*-g*

14 A B A* -B* -A B -A*B* -A B A* B* A B A* H*

15 A -B -A*B* A -B -A*-B*A B -A*-B* -A B -A*B*

16 A -H A* B' A -B ~4*-B*A -H A* $* A -B A* -B*

Table Fig. 1 diagrammatically illustrates dais transform for a simple case o~ 16 elemeaats (~T ~ 1 ~ in a sequance A rtprcsentod by dots at the toy of the illustration, these being reordered as shown by lines into a sequence A* represented by dots at the bOtt01114f the illustration.

JUL bb "~ 15: ~b 1-K N I h'H I tN I5 bl.i 'f'~'1 ,3b1'f I U b 1 ill J '~5,5 ~4'fb h'. IOy~~ki Address Bit R1 This transform ttvarses address bits, represented as binary numbers from 0 to N-1, which can be used to identify the elements of each of the sequences A and B, to produce new constituent Golay sequences Ar and BT respeGtivrly. Thus for example for N = 256. tho elements at, az, ag, .... aZ54, a~5, a~ of the constituent sequence A can be identified by the binary numbers 04400000, 00000001, 00000010, ..., 11111101, 1 i 111 I I0, 11111111 respectively, which are reversed to give the binary numbers ppppppp0, lppppQpp, 01000000, ..., 1011 x 1l l, 01111 l 11, 11111111 respectively, correfiponding to the elements a1, alzg, ate, .... atg2. atzg, a~6 respecdvtly forming the transfarmcd soquenee Ar. the soquan~ B is transformed to the sequence Br iu the same manner_ This is in elect a pormutaslon of the positions of the constituent Golay sequences A and B, so that the transformed sequences Ar and Br are also Clolay sequences.
As described above in relation to sequence revot'aal sad Tablo 2, the preamble sad signature can be formed from the o4mstituent t3olay sequences A and B and the transformed sequences Ar and B~ the lattear transfotnxed saquenecs substituting for the transformed sequences A* and B" in Table 2.
Fig. 2 diagrammatically illustrates this transform for a simple case of 16 elements (N =16). As in the case of Pig. 1, the sequence A is represonted by dots at the top of the ~0 illustration, and these are reordered as shown by lines into the sequence AF represented by dots at tho bottom of tho illustration.
partial Bit Reversal This transform is similar to tlye address bit reversal described above, but reverses only a subset of tine address bits, again represented as binary numbers, without making any change in the positions of the other address bits. For example, tho most significant one of the address bits may bo unchanged for each element of each sequence, with the othex binary address bits being reversed in the mlanner described above, with the r~,qult that the tranafa><m reorders the elements of the sequence A in iwo distinct groups to form a tzansfornxd sequence Az"'. The elements of the sequence B are reordered in the same way to produce a transformed sequence B~. A~ ana B~' are again eonstitue~nt Golay sequences which can be usod is place of the sa~onoes A* and B* or Ar and Br as described shave. Orber partitions between the uncharrgtd and changed address bits can alternatively be rnadc.
Fig, 3 diagrammatically illustr'soea this transform for a simple case of 16 elet'~nts (1~1=16). As in Figs. l and 2, the sequence A is represented by dots at the top of the illustration, and tl~se are reordered as Shawn by lines into the sequsnx AzT
relmesenaed by dots at the bosom of the illustration, the reordering in this case being in two groups in JUL bb "~J 15~ ~b hht N I h'H I tIV I5 bl.i 'f~i ,3101'f I U b 1 >31J ~3 ~4'fb h'. lb~~i that the most signiftcaat bit for each element address is not changed, and the rem~a~nidg 3 bits fox each element address ate reversed.
g~~~ .~] 'ti nin This transform concatenates two (or moc~a) sub-sequences of the evlaments o!f each of the segueztces A and B obtained by decimation sampling to produce transformed sequences As slid B$ respectively. The traasforxned sequences A~ and B3 are again oonstitucat Gotay sequences which can lx used in plea of the other transformed sequences as dcscn'bod above. For exampie, dividing the sequence A into two (even and odd) sub-sequences, its elements a1 to an are reordered as:
A3 = ( al, ~, ..., aN_l. a~. Vie, ..., aN ~
and the sequence B is similarly reordered to produce the sequence Bs.
Fig. 4 diagra~oa»>~~y illustraus this transform for a simplb case of 16 elements (N =15). As is Pigs. 1 to 3, the sequence A is represented by dots at the tap of the illustration, and these are reordered as shown by lines intro the sequencx AS
ropresented by dots at the bottom of the illustration.
The above are examples of tntasforms that can be used to permute the elements of the colnstituent C3olay sequences A and B to form new constituent C3oiay sequences, and It eaa be appreciated that numezaus other transforms can similarly be used ~
addition, various c~binations of these trattsforlns can be used. For example, the elements of two 2Q of such transforms, or of one of such transforms and of the original constituent Golay sequences A and B, can be combined is an exclusive~r (XOR) logic operation to result in further constituent Golay sequences Ax and Bx. For example:
Ax = A ~ Ar : ~ al ~ arl, a2 ~ art.... aR c~ 8~yr sad similarly for the scqurnee Bx.
It can be appcecisted that although Table 2, and its equivalcata using other transformed constituent sequences as described above, provides a reduced repetition of sequences within the overall sequence of 16 x 256 ~ 4Q96 chips, this repetition can be fiuther reduced by use of different combinations of the transform sequences desedbed above in a hybrid concatenated manner. By way of example, instead of the cycle A, B.
A*, B* which is repeated four times as shown in Table 2 for each of the 16 signatures (determined by the abseaae and presence of - signs), a cycle of 16 ori~al, transformed, and repeatedly ttattsformed sequences can be used to provide an effective sequence o;f 409fi chips.
One example of this is giveat by the following Table 3:

JUL bb ' ~J 15: 2b hK N I h'H I t_IV t 5 61,3 'r~1 .i101'f I U b 1 lily '~.5 ~4'fb h'. l li~i A B A* $* Ar Br' A*r g*r A~ BS ,A,w~ BrtT~ A2t gZr A~ g*7.r .
Table 3 Ia Table 3, A to H and A1 to Hl repr~a~at respective ones of I6 constituent sequences produced ag indicated by the second lint of the table. For example, the sequence H is constiWted by the soquence $ after sequcncx c~cversel to product tlx segnenoe B* as described above, this then being subject to transformation by address bit rcrr~ as dcacdbed above to produce a sequence B*I. It can lx appreciated that the concatenation alternates fast tb~e A and B constituent sequ~ccs and tbeir respective traasforrns and then the sequence reversed transformations. Table 3 does not iadicate the absence and presence of - signs representing flee I6 signatures. Using for simplicity the nomenclature A to H aad A1 to Hl of Table 3, the (allowing Table 4 illostraits a possible allocation of 16 Hadamard-W alsh signatures which are arranged to facilztate non in a high Doppler frequency environment:
I A B C D E F G H A1 B1 C1 Dl El F1 CIlIll 2 A -H C -D E -F Cl -hI A1 -B1Ci -DlEI -F1CI1-H1 3 A B -C D E I' -G -l:IA1 BI -C1Dl El F1 -Gl-H1 4 A -B -C D L -k7-G H Al -H1-C1Dl Ei -Pl-GIHl 5 A B C D E -F -G -H A1 B1 C1 DI -EI-Fl-GI-H1 A -B C -D E F -C~H Al -B1CI -DlE1 F1 -GlH1 7 A B -C D E -F G H A1 B1 -Cl-DlEl -F1G1 H1 s A -$ -C D E F G -H A1 -B1-ClDl -ElF1 G1 -Hl 9 A H C D E F O H -A1-B -Cl-DlEl -F1-G.1-H

IO A -B C D E -F G -H -Ai>gI-C1Dl -E1F1 -GIH1 11 A B -C D E F -G -H -A1-B1C1 Di .-Bl-FlG1 H1 12 A -B -C D >r -F -G H -A1H1 Gl -DX-ElF1 C~I-H1 I3 A B C D -B -F -G -H -A1-BI-ClDI EI F1 Gi H1 14 A -B C -D ->rF -G H -A1B1 -ClDl El -P1G1 -H1 A B -C D -E -F G H -AI-B1Cl DI El lsl-GI-H1 ld A -H -C D -E F G -H -A1B1 Cl Dl El -Fl-CallHl Table a is Iasread o~ using transformations of a single pair of constituent (3olay sequences A
and B as described above to produce longer effective Golay stquenoes> this can also be done by usiag another pair of constituent Golay sequences C and D which are not J~ 4?b "~J 15 ~ ~'r hK N I h'H I tIV I5 bl.i 'r~l 31d1'f 1 U b 1 ~il'~ '~5.3 ~4'Ib N. 1~~~13 derivable by transformation from the pair A and B. Thus for example a cycle of four constituent sequences A, B, C, and D can be repeated four times to produce the 1b x 256 ~ 406 chips overall sequence lcagth, with the 1b signatures being provided as described above by Selective inversion of the individual ones of the constituent sequences.
In addition, the traasfo>rtnation techniques described above can be applied to the sequences C and D as well as to the sequences A and H. I~owever, this use of additional seguences C and D results in increased computational complexity and dots not appear to produce improved correlation results.
Fig. 5 illustrates two stages 10 and 12 of a known C3olay sequence generator which eau be used to geaeratc the constituent C~olay sequences A and B. 8ach stage 10 ar 12, shown within a dashed line box, has two inputs and two outputs, arid the stages are concatenated with the twd inputs of the first stage supplied with a binary 1 and the two outputs of the last stage providing the sequences A and B. Altktough only twa stages are shown in Fig. 5, in fact the generator has P = logzN stages for providing sequences of length N. Thus for sequences of length N = 256 as deaulbed above, tb~e are 8 stages of the Golay sequence generator.
The generator stages 10 and 12 all have the sarnc arraugenacnt of a delay unit having an input coupled to o~ae input of the generator stage, a multiplier 15 for >anultiplying the output of the delay unit 14 by a coefficient W, and cross-coupled adding and subtractingwnics 16 and 17 for providing respectively tho sum and the difference of thea other input of thd stage sad the output of the multiplier 15 to constitute the outputs of the generator stage. The generator stages differ from one another in tlx delays provided by the delay units 14, these delays being powers of 2 fmm 2o to 2p-1 and being amnged in any order among the stages, and the weights W which in Fig. 5 are indicated as Wl and W2 for the generator stages 10 and 12 respoctively. For binary Clolay sequences the weights W are binary weights of value tl.
It is observed that the choices of the weights W and the ordea of the delay stages of the generator can be selected to paovide optimum properties for the resulting constituent Golay sequences A and 13.
Fig. 6 illustrates two stages 20 and 22 of a known Clolay scquenco cornelator which is referred to as as ef>Ficient Golay correlator or EGC. As in the case of the generator of Fig. 5, the PQC of 1?ig. 6 has n stages where n = Iog2N and N is the sequence length, with each stage having two inputs and two outputs, flee stages being cancattnated with an input sequence supplied to both inputs of the first stage atod correlation outputs Ra aad Rb pTOdt~ed at the ou~uts of the last stage. Each correlator stage includes a delay uait providing a delay from 2o to Z~-1, a rreultiplier with a respective weight W of ~1, and cross-coupled adduag and subtracting units, in an arrangement Jl~ lab ' '~J 15~ ~'f fK N I h'H I t:N I ~ b1.5 'f~l .i101'l I U b 1 lily '~,5 ~4'fb h'. l,i~~3 which is similar to that of the Oolay seduenca generator except that tb~e delay unit is provided in the other input path.
The use of the FsGC of Fig. 6 for the ItACH of a celhilar communications system are lmown for example frown subnl~ission TSC3Rl~i3(99)205 referred to above.
hog 5 addition, reference is directed to S. Z. Budisia, "Bffiicient pulse compmasor for Golay corciplcmentary sequences", Electronics Letters, Vol. 27, No. 3, pp. 219-220, Jan. 1991.
As these aspects are imown in the art, they are not furtbve~ described here.
Fig. 7 illustrates a block diagram of a preamble correlator and sib dad according to an embodiment of the invention. Such an arrangement is providod for 10 example in a BS nxeiver of a cellular communications system, and it can be atoll that a complame~ary arrang~eme~ac, with similar address per~oautation to perform the transforms as descrlbcd above. is provided for producing the concatenated preamble and signature.
Far constituent soquent;es of length N ~ 256, the detector of Ftg. 7 comprises art 8-bit bidirectional counter 30. an address permutation unit 32, a 25b-sample duel port RAM 34, a Golay saquencc oorrelator 36, a multiplexer 38, a Past Hadamard~Transform (FH'I~ unit 40, e~ a clock and control unit 42 which supplies clock and control sig~aals to the other emits via clock and control lines which are not shown. Input samples are supplied to an input of the ItAM 34 and are stored thezein, ax addresses provided by the unit 32 via as 8 bit address bus 44 as fiwtha described below, in sots of 256 samptes correspotrdiag to the Golay sequence length. The sanuplas are read wt consecutively from the RAM 34 to the cornolatar 36, which has the known EGC form indicated above with rcfsrence to Fig- b. The carrelator outputs Re and Rb are supplied via the multiplexer 38 to the 1?>:Tl' unit 38, which serves in known manner to provided a final ZS detector output for example in accordance with the signatures of Table 4 above.
These signahues are of length 16. so that over the duration of the preamble of 4096 chips ld sets of 256-chip samples are processed ittt the units 3G, 38, and 40 in a substantially Irnown mauaer. The units 30 and 32, operating under the control of tho clock and control unit 42, provide a corresponding synchronized cycle of 1 b address permutations for these acts. in accordance with tb~o transforms described above and for example in the manner represented in Tables 3 and 4.
To this ond, the addres9 permutation unit 32 is amatlged to pxvride a cyclic selection from among different sets of connections between its inputs and its outputs, as is m~esented diaaatnmatically in Pig. 7 by selector switches at the (8-bit wide) input and output of the unit 32. Within the unit 32, these conunections eaa ba in the form of direct connections becvveen tire inputs and outputs corresponding to the illustrations of Figs. 1 to 4 and their variants as dcscn'bod above, for example as given by Table 3.
The sequence reversal hansforms (indicated by the * in Table 3) are cbnvanieritly e$oCted by i~eversittg JUL 4?b ' "~J 15 ~ ~~i hfl N I h'H I tIJ 15 61,5 'f~l Jt01'f I U b 1 iii' '~.i ~4'fb f'. 14~~i the court direcdan of tblo counter 3Q, so than samples are storcct in the RAM
34 at a rcvcrscd sequence of addresses from that from which thcy are read out to the correlaoor.
For chc other transforms Ce-$. A~, As, and A~ in elation to the sequence A) represented in Table 3, rcspccdvc acts of direct connections ara selected cyclically by the unit 3Z in accordance with Figs. 2, 4, and 3 respectively, in cooao~pari~son to straight through (i.e, act permuted) connections for the sequence A.
,Accordingly, the various transforms represented in Table 3, or other tr~sfom~s that may be axed, can be easily provided by an atraagement such as that of the bidireetional eoun~r 30 and address pcrmutationl unit 32.
14 It can Ix appreciated that although Fig. ? and the above description relate to pet'mutcd storage in, sled consecutive read-out fmm, the RAM to provide decoding of the transformations described above, these oporatia~s could be iaterchemgcd with equivalent effect. In additioa it can be appreciated that substantially the samc operations can be provided in substaatially equivalent manner for effecting the transformations in generating the transfa~cd seque>aces. Thus for example the correlator 36 of Fig. 7 could be replaced by a Golay sequence gerr<<exatox, having the form of Fig. 5, whose output is supplied to the RAM, an output of the RAM pro~d~ng the generated and transformed sequences, with a similar counter and address perlmutation to that shown in Fg. ?.
Although particular cmbodimencs of the invention and various altarnazives have been described in detail, it should be appreciated that numerous modifications, variations, sad adaptations may be made without departing from the scope of the invention as de>fintd in the claiu~ns-Jl)L bb "~J 15: ~i hK N I rH I tfV 15 61.5 '~~1 ,3ldl'r' I U b 1 liib '~.5 ~4'lb h'.15i'~f P.IsP'FNDIX
Ts~-RAN working group 1 meat~nH X13 TSGRi~(99)~06 Nyna~shamr~, Sweden March 22-26, 1999 Agenda Otem:
gouoa: Eritason Tltles flew RACH preambles with low aulo~orreletion aidelabes and rsduoed de~Eeoeor t:ompfsodty Document for;
1 Iatroduc~on ~ pie pssc or era assdaa~ gate b~c silt iormae p~o~a ~r vWD ms tba oat~6 code ads (11-Tbe ps~~Ms ee~dsn era ~~rm~v~ ofl~n~ 16 eo~ks ~m6ola. wh~b arasp~ad by s eo~nm~, 2Sds~ long p~p,~t cold saquesos oalledprst c~o~ nn een! ebara acs 16 dv~a~c~t si~arcno~e, a6t~Oed ~ dr' oil sat olbiria~y ~o~a~l Gold se9nssson a! ~h ~6. bY ~ ~ ~ with tbt oossnnot ooa ottm>>txW (Lrj)I~, whee~e~~.
1ba T~ txessmiuioos of ti» saadom aoorss bra eaa slap at a a~ wml3~ed dmo a(wavers s)ots~ as sy,~~ so ~e tismo sync o~'t~a poda~ OC~4'8. ~a pd~y OCR Exams syx it; e~ae~d tldbdt die c~ s~
porpped~s be t~s V8 Tb~d~s ~a saadom aooas p~mbles ass teoeiwd ac t'ho bye station st >5e betas v9f eeoh aomaa slot keerraW vlth d~ ticris uaos~taiaty t~ ov the ~nd~iP p~op~don dalsY~
?h~ : random moans pCSarnbla couc4ndioa allows Bed caal:sttdon a~'tba bash of ooQaiv die 6tse s~av tsadom aoaess rsosivor if tbit elme os~oa~ fs ~ 255 e~pr. hto~uw~ >~
sttto-oo~la~ou slddovm aL ~ codes sri ratla~ hiy&, whip ntas<s ~ t~ R~ P~ ~ d~sctad si wiva~
time paddoas. In o~ wands, the presmobla detectiomyobib~y at ooem~t 4uaz !s debelo:aomd foi mad~t ~o bigh ~4so.ao~a rat~.'~arefore it !s desi~ble ~o fiod aa~r ra~oma ao~ ~amabk oonsauetloe, rwsnld silo ~oduoc an ortJm;cwt rat oaf ~eaa0.bk coda with much lanvx aperiodse arum-corrslatfon tabdeb6es, QB:a a~ese n~had,~er Colay complemenl~ry seqiat~ces 'fhe srew RAC>~ ~rtbt~ m~s bated oa e'~r:,p~cadoa oot~y atom fha Oo~r ooa~lammf~ plies. I7~ as~a~
pe~cpeety a? the bln~r seqmooss from 8ys Qoi~r cooaplsm~ !~' n that tbo sum d1 ds~ apaiodio auto-ma~aetativrt lbmaslems eq~mla arv lrOe alt noa~m t~ s~db. ?!~e Getay sequsaoes man he aeausaavd !bc anY 1a~ L= ~.'N is aair potitiw i~r. and also for laths i0 and ?.6, os Lot nap oomtrinati~on of those tkss laa~. the comopkma~cy ps~. sv~ sequ~ooet axid~c some ~ p~d~ee ~ maloe tbe~s amsctiw as syscwaisztiao codes: f)rey l~
fowr ~rivdnc auto-cotrolatioo sidetobes, apd throe is a ls~e oaaabar a~iheaa fir a ~ ovds t~dt.
If dm aeqwsvss ara of let~tth L=~~; tl~ers is a 1 ms~Od fDlr d4~ coms~s odpolyp~e o~les~a~ Pmts of sagu~es, whemhe Oolyr oom~pL~nt~y tsquaacss ~t jntt a apedt~l. 6asseY rate.
Tl~at cetutrnaboeo is deS~aed by the l~oflowias aeomaivo tela8,oo (~].
6oU~ ~~) ~) ~ Rn~W1 + Ww,iw.yw>
bw~~ ~ Crl ~ ' ~w'~iw~1~W ) ~ .

Jl~ Idb 'Jy 15~~i hK NI h'HItNlS b1.3 '~'~'1 .3101'f IU b 1 t3lJ ~3 '~'4'rb h'.lW~i k=Q !, 2, ..., a"'-i, re= i. 2. .... )V.
r, pw ~ Z , awlJl7 god b,~le7 el~a two aampte°~ a~~
8(k) is the groaeciotr aata~ >~o~loea.
k 5 an iate~ rapr~n~'~ ams tosla, n is d~ laenmwe o~m~D~r.
D" fs a doLaD'.
p,,n~l.Z...~lV.ii~Y~°f i.2,...,JvlLl~.
W, is an oo~isoc >m~ °~' If ~, has values +1 ma -1. the b~ tciod~ ~ obadaed (31 Ao e~c matod~d ~ d~ Eli m sfhe oosc~rlsoyy ~qs °~ ~ br~G4 ~ ~ tl) ~
~'raa is less 1.'~ >mmrp~ ~ ooedo~tln~ s~rl ~(JH aiaWr~swrsl~ wllb date trao oomphaesumm~r seqaa~ost a~
gad b~;. Ths trro ms>~ ~ ~ ~ t""o ~a ~~~ooca~lom R~,.('~ and pd~l. svoh a ai~ai ~tsr w$1 be caDed ~e c3ony Cca~iioor . ~ ~ t~ ~c aid ~tiw to agy Pclypbas° ~P~ ~'Y tl~ Woma6ohed >~lser !~ oooDnQ>~c ~Mao~ieaa w,"
eas w..
o ",e~ ~ ~J
n, ~ ~t a.'~1 - ~ ~~°'~ -w,' w,' Face 1: Gol~ Carsetemor ~CiC~
~ beaus In P~uoc X ~pe~e~ ~e oawa~u~diai d~ l~s'~ D, m°~' ~ cumber aL~oo~r tie >tha HOC Gt aqml ID to~GLk ~ is ~ ctrn~onw~ >~ ~~ it would be L 1be »mba aE ie tba 11QC 4 Z.~o~>.,~la in,~a sbrai~tosiu~u~3 t~m~ud i~lec fi~a~oa lt.vonla ~s Gi.1be atoa~r a~ mem~r slemoaatt taqnhd ~br ~o ~t3c is L.1 t.~+~+.. ~,v,~. ~a same as ~os a~sa~ts~lae,v~d ~>wmrwa oia da~ie mr>~8d 5r1»oot~pvoditts W orde ad' die aaa~rle~mt~y r~q~d.
3 E~cient Golap ~oatQr with redrxted memory ~.be e6,e.vlam ~..sp.orAd aviqs s of imip~ne d~Aat >ze Am~ed o~ be h~Q'",~
eh~c. Ic is po~l6 ~o dal~w med~e B~o~!
c3oiay oocte~Iatoc ~tm ~r~s6 msmocy '1'bo l~c,~ rednoed >memory is butte oo,~
ce~~dao e~ a clelby >»qaea~o. of lad L~Q~~I T"",~ iu ~S so-allod "bt4~" ~4 it. as s f~sao~am of ~~u aho~t oons~~plemsa~e~t aqro~oet A(~ cad ~(kl a~l~ Tw" Thb ~ieedon is a ~ ooo~aqusaca o~tbs a camssenodoa tl~, wwch oaa eca~Y staatt ~ anY ooas~I~t~ F~ ~ ~9~0~. Namdp, if d~a ~alda! vesbats °d~ ~ ~a(k) sore bloee to ba ~ _ ~~. ~ 1, ~,-.., T",,r~h (Z1 wl~seA~ and ~Clh ~ d~a tea SPY i ~T~.r,~ dry Psit°~oo~pbemea~
taquenost ot'ftnt~ L~~T.,.. is a~»r. Note that all ma dada D. i>A tl) s~ be soled by tbs >ro~sh of ao~dcueot scqumcas (T..,J.

JUL bb "~J 15: ~J hK N I h'H I tJV I 5 b13 'f~l 3b1'r I U b 1 Lily J53 ~4'rb h'.1'f~~i ga .. ~ the oo~s~eem~ sequtldoa are or lath i'.~4, am poromsaews ~oee. P" eed the ard,~.~eao~s w, sot o~! lao~t~ lb it dse resd~g ocoaP~~ ~' a~°uid b~ °~'ta~
.109~'11~ s~J' ~Iaoa~ o~ B t~
~ ~ ~' vEdeh an ~ael~lsxad so~o~ tp some ot~aleac blur "~1" ~o6aa latRa de~Odi~ on eim p'on ' P~.'~ °~°~ ~ d 16 Cso~of teak A0q6, ba~'~
~~oov coestitnsot Mk3 ~ ~ e~~ t~ a °°~moo~ i~xlavbas ~nrcdo~, oon De ob~d by obooa>~ ~ sia~
pmbmu~ve vectx o~1'~ alon* wriah 8 sppcY cboae ~ra~das ~e_ 'I7f~ addldoosl 16 ocd~of~1 t~ ~1°f 4096 hx~tr~ ~ ~ aunt seqernaee Ate' ad B(x1, bot iota~~d:AOOtdsag ~ s~ ~f lltl'~' cam be obedned bY ~
a~flb ~ ~'?.
~(~= A(~, I6.0~ 1, a..... T",~-1, sed ~ the sande pamno~ and w~doa at far d~ brae xc ~ is 3~so~r. in weal t>>rre rse J2 cat~osoad tiobpr s~uo~s ~ 1~ l~:m~ dse balulsmolt coy ~~~ Z° pi°
~ pe°tble 00 ~'sa~ls ~osooai (3oln~ setlm~,. w~l~ere J~'J~'", the sec of i6 aad~oal t3olary x9~~ of lad ~ ~ ~ t° me above >r~ w~ cm be uisd is ~ is ~a ill Tebls i, as a o~twro oonsd~ aotc431ntt>ata87t s~ AUK ~
~
ad lash 256,'1't~e adds~nal set o~ 16 oc~o~ t"soLaY ~ ~ ~ ~° be obtdmrd b~ ~in8 ~? ~ ~
and wde6At~ ~ ~ i. a Aft aobd Bfxl ~ ~B°'~~ ~° additional fex is ~B~ to d1e ll~st ooG
?~bls x: Ehst 16 ov~oml Goth ~l~a of l~td~ ~
a.sss~
. B B A B A A .,..
A 8 A ,A -B a ,8 ,8 ,rt ,~' a A -rt8 . A ! ) A .v8 A d i a!A B ,a A ,A ,A ,~
A ~l B A 8 -A A a A a B B w A ~A .IIN4 ~ .A -A ,A -1 A A ,8 A ,A D A -A,a w A 8 A A -B ~A B A ,A
_B w A D A ,A B

as s a a s,A rs a 3 A ,8 -AA - a -~rl 8 ,A. A -B -B
A -A ~ s H,~ A a w B
yet A .B ~,.A - a A a .w A
,~

T6e itAG33 p~bie oerreietoc writh redneed r~xY. ~spo~n6 ~ 1~ ~"° sae oCZ 3~ osd~lopc~lbl~ f>t iWvn in Frgnrs a 'ills ~ Y P~ ~aoa~wd ~gaa~ma in dds sod is ~e s~ a: !ar'.~e 1~
Opadeoo~ deeded is ~. Howaralc, IM meat aio~bsc of addses and mutdp~s is siY
dua bo ehe nee a~B~C inseeed ofpotefemble spoode matcbod 9l~ar J UL bb ' J~J 15 ~ ~J hH N I h'H I tN I 5 bl,i 'f~i .id1'l I U b 1 ail J '~.5 ~4'lb h'. ltt~~Li mC
aElo~ Z?6 ~r6~~_ ~3ia~r~plw w ~H~t_ bi aaooYi i 1i~81 F~lZ~~~l~~~l~~li~l~d~~m:~t~
Ths isoeGaotioeil~, in eO~DO~n foot' d>te Id o>r~u~~1 pea. w1~ the i~a~rlq6 ll~oe hf~ b eo>>mnol:
~ tils atf>ka li ort>l~ols~ pra~ei. a'xablW it um ead~ 6e xea d~
~ef~?= t0. 0.1.1. 0. 0.1.1.. 0. Ov 1.1. o. 0.1,1,1, aad h(xl: t i, l, 0.
0.1.1. 0. ~. ~, ~, 4 0. ~. 1. 0. 0)~
$~ IE 11~ ; t~QOE ~ ~0p1, Gill ~01~ 6~ ~i ~~C ~. g04' C, s;~~o = sis = c~. x. ~, x, i, -><, -i. ~. ~, -~, ~, -1,1, ~, -~. a ).
~ set of ?56 e;ec p~ of ~ola~tllmen~ Cie~r seqnecoeuttkl aed H~ toesnespoad~
to ~ xt of 2i6 amll ~ lit dG~aed 69 n). ~ecs ~e pawn v~e~,ps h oo~n~on far as pails tmd hr ~ bar .~~= to. ~. i s. ~, ~. ~. 3). <4) ~ the o~enspondia~ 1S6 wroiaeacloe ~h'~). y = G.1, .... 3x5, ace died au die d-b1t bimeY re~e~oos o!
fa i, s. ..., ass}, ie.
~(vll) w ~lja"~'~ . t~ - O.1. .... 255. a =1. Z. 3, ..., 8, (,5s) wst~ese B.fx) is the rib bit in the 8 bmWal~ >ai>a~ repct~an~loo oisollte ~
ire.
x xo'~B,~(x)~2"~. (3b) Noes 8su w;l 2S6 aoesapapa tae be dateooed by ncio~ the asooe ooadaox siiowa in P9Nso I. Iry oaty ~
vooe1V~ .

JUL bb "~J 15 ~ ~J hh' N I h'H I tN I5 b1,3 'l~l .5101'l I U b 1 Lily JS.i ~4'lb h'. l~J~i~i ~'mplleaoatmott~tfion comple~t~
'mss ~pk~e~n ooaop»ty of the bmplc a~RA~ t !s r ~e~od d~ to ids cw o~ 8GC
issteed olpca~mbb oodd maraet~ed >~ Aasr~a tmt dse a>hbs of new aedsooav~l pr~6ies bated oe Qolry ot~ocy srqoaoors (6C~ and ~ the wme (iya bt the sere of the sm>hot ye~bld~
based ea eoaaanoetad cxtho~al told (~. ~ ~Pla °1' °f ~"
°°~~°°~ ~ oioo~tators asn be oo~vd m tho falloari~ way:
s) TM numbervf addaat ~ 3Z (i16+1~ for the OCS. ~ ~T1 (~x+16) adds f~ dw OOS.
») i'ea ~ o~f~ ~ c~~+y ~Ir tea c~ a eo sri ~_~~ roe aye oos.
e) "Users ie s ~ (s~imob5 ~r G~'~ ~,~ ~ ao zexar float UGS,.
Tbn banEths of aei~y Iiaa us >be s~mna m bes>b names.
Ape~~fG auto~ox~elst~n gropex~tea Hecida tb i~od ~o~pl~m~d~ , ~ ~ pbe9ea oa Gol~r eeq~o~t ooh much beaa pedhis ~ of tehc ~o~aoowbeelnas >roao~oa~riva sidefoba Q~dAE), w6ea com~amed wifi~'ths as~elot perk codes booed oa c~raYn~d oelbo~aoml Geld seq~roas.
As x best ~aampl0. the apeceodisr a~ba-datn~lom !be oaa ollhs ooocdaaad t Gold lei wR~eh the old sere Goe peeamWr spn~ oodexi a bra le P!»e 3 in the ~ l7ais theuld btoompaand ~ the new sronusbag ~ sm4s>es~es w~ cod se~oenoes A and 8 defied by (1~ (~) and. as as Vie.. W,~( 1, -L 1. -1,1, ->r,-1~ 11.?hs apssiodo aato~ouel~ ta~>bb aaw earls 1s sbowa in Fios~sr 4 ijntbe sue. As ~ta bs eau she Copy xKloeeoes l~tv~a stanch bettor asaGD~ca~eldon pto~pet~e.
TJbs MA9 !6~ xB tha booed ooihe above G ~eedlnE node ss~e tad io ~'abls 2 lies bew5ts of dre Gotay ssqecacee fa tai o! rnMAS lm aliaas.
'1'lb4s 2: MAa~s ~ ~mb~ a~sP~$ ~ ~ ~~i ~
~y ~ c~eran~d otirmoaoo.~
voyd Nltmber MAS of 9 or Oa~all~ea b0C1~1~C13 idx itl~4 a ~ ~s z a X18 "gym ~s psea~es s~s~e ant ~pleoe~ asywr~coaaontt bo the base atxdob r4Ce~ss beorose Ih. v8lses th. basic i~aopant bate s<d~wt ~& ~ w~ as »noesnia4r mby the sounds pnop~ion daisy baswaon tae bane s~atioss and 1J8. ~'bs c~enc aa~ae~o ~a ~AI~D~D is ~mc the roip asitpr ~t ac mou 2~ dt~t ao ba able to .
tha pnsposd simpTi>3ted sacei~as cl<octolr;. ao the ado sam.oaasdalioa >of r~Om antes it aof s»rt ~neeeac only is tb css~ion a,l 2~5 6>~ 1be ttrsin lob0. Z'he sssud:nman abeoluEe val<re~t oaf amoo-ooaalatlon aldalobea In dre ie~ioas ~- 355 daps std xsdh ~obie are shown In ?abils 9 fat the pss~dei~b~ (3oleY
asxd aoma~msQd ~opomal Ooid a~sxt dd ien~ 4096.

J1.lL bb "j'-J 15~ ,51d hK N I t'H I tN I ~ ~ 61,5 'r~i .ib1'f I U b 1 lily !53 ~4'rb h'. ~~t 'habi~ 3c DdA~ m t!~ x.156 e~s ~' P~a~ t° ow p~rlieot~r ~a~k sues °°d~.

of MA$ 1'inmbot I~J1S
of oova~rutsa 16 Sl 1 T3 3 y43 Prom 3~bla 3 it am ba ~odosd drt 4omy r~qa~abrt l~ abort 33 Mmes b~ ws~o~l~i4o ~d~a~ea t6ss the oor~cd O~om~ Oabd esqw~oee, is eb ss~oa ~ 955 c>Mps d the rf>~0. lobe.
a tr clr~r dmc ~ ehe p~omar ood~ ~a above, ms Go>iaT seqnrooa are s~rJae:
l~Ibi. ~s m.~amam abaolax vama os~o~ooaaretmlo~ ddefebet ~ t>ba xe~on,,~ 33S ~avaoa tba m~ loba m svtlmrOad for dl per. aab 16e C~l~t ~aed ?.~6 piles a~oamaitoeec yes w and 8 dmd by C4) aad !,~ fot al13y2 oe~o~xa! ~a~mblx of lw~fa d096 oo~ond9nE ~o cac4 such ps5r of om~6direa~t seqnaoces. a~ fl~s aunt pry bated on COnc~e~sd Orthogonal c~o>La sew »e >~ Via. ~c~e ~ ~m.ra ~ ~at~ ~.
~c~.sres~ ~aea ~.t» ~ ~.as ~. r.~r.~ ~8 ~.
t3aaf5~y Cametmoeosted seqn~cat Or~oio~l Gold ooas~awoes i2ao a s io~t A.~a~a~ MAs !h ss9, ><b00 bdAS b 14190, tzao t I~~AS ~

9591 of l~dAS
vet arr; above ST6 ~ 50Q.

25b 4 3 I ~ I ~ I I

Table 4 a6o~s ~t all i 19Z potdb6a C3olaoy ~' >~ ~. hart al~r » ma~dmvm a~so-oo~o~
s~obes. ~'6o smars~e MAS L 39. and 6591 of me MA9 rahxa aar bean 2~' tad 3"1.
A, sibs, but rrtb~r faa. aompaisow bsa~a chs trro difi~c p~m~ dead Gsn Is!o dooa by eo~pmom~ d~ sva~G Mats. Tbc Cad Ga~aa~eotoed nai Ovfd p~b~s hays au sw~e I~AS 18 liana (66W3'71 h~ draa ~c (3day bwd p~bl~s.

JIA. 19b ' J~J 15:.id hh N I t'H I tN I5 b13 'f~l 3b1'r I U b 1 kii~ J53 ~4'rb h'. ~l~~ti ~~~On A sew iec of RACE ~ P~oD~ ~ y°° in ~_'n~e beaaHs of tbo ~vaml~
soda, bored on Goyy ~°n°°d. a~a:
r Tha lAav Daft f~Y ~ a daocE~ hardw4re i~lemel~iou. tis awmt on 9re nao~ of amlaptiaa and adds re~~
a 13e m~bx olav~les ~re~mb~es ie doubted. to 5192.
~ An ai9a otitw navp~s bm B~ ~o-oansE~dion propa~as. ~ ~ far aLu odd pie a~ ~
sad ~1 ~ ~ ~ ~ b~dvbrs ~ me peg ~ psaa.
e~ei~ powatfa~b baser rE3b/No pedo~.
~Ce3 si.~a. vr~~ s~a~m~ ~~a o~
S.ta. "~a~ea~ Ps~ ~ tae Gol~~ oe>oenDle~ . ~lec~e fed, voJ.2?'.lfa.3, ~t~a~ ray. r.9~L ~1~ ~
~.~fY~s ~~ ~w~ ~ ~. ~ '~ ~, ~ y~'s ~W ~ ~~1.
~Ip ~1 A~01~! ~~i1~1M1~ ~ ~ 1~ ~! ~lsll~ RACH ai' (e~E + p~'~k ~ aode~

JUL YJC '77 13~J1 t'K IVI Y'hiltfVlS b1J fGl Jl~lf IU b 1 1317 7J.) G(i/d t'.GGiQf .........~.......,..i..,..... .... ...~ ... .~;..........~....,...
._.............
' .... v ..... ' ... , . ' ..
...,.... ...~..... ..,.;.....
..~ .
....,.,..;.~.- ... ~ ...... ' ......~.; L.......;..._................j...."" t ...., ....... ...... ...... ...... ....
...... ...... ...._. ~ ......1..........i..........;..,.......y.......
....... ...... !, ..... i. ...., ~'~ u.u.~.........o..........~...u..u.(.,un.
.. . ..~ . .. .. ; ( ..... .._...E .........i...,......~ .........y..........~ .... .
,... .. ...... ~ ...._._j..........~
...................j..........;..........r......
.. .. ..;.. . 1 f __ -mesa sees aeaQ gee sme oo as eem saeo p~Ce 4~ A~os~a a~~o~op~em fop !fir eme e~ the new BACB peeam6la I~ ~~ Tnbk ~) i 1 .~
....... ..... ..... ...... ...... ~ ...... .......,..........k........
~ .... .,. ,....... i"._... "~.'.......,i........ v ._._.~.3....... ~ ... ' .....
.. ..
-..P......_...(.....
...,.....;.... ' .. ~ . ' .. ' ... ~ .._. ~ ...
.........~~........~.._.......;...... ~ .......j........ ' ..... .... ; .....
.,. ..,..
,b ....... ........~..... .. :..~. ~ ~ ... ~..........i........ ~ ...... :
.....
. ~~~ ~ ~ ~ ~ j , i ~ ~ ~, hs i t .. . .. .. .. ...
.._.... = . , . ~ . .. al'wl~,', ~ ~ ....i....~' i........
f~ ~ fee eoC Ie1 1E1 !b1 Iee 1f~ llpp K~
$: ~10p 0~ ~$ ~ ~d1 t~1! ~ Vi~~lrpld ~~
. wr

Claims

WHAT IS CLAIMED IS:

1. A method of producing an extended sequence from a pair of constituent Golay sequences A and B, comprising the steps of:
transforming the pair of constituent Golay sequences A and B to form at least one pair of transformed sequences which are also constituent Golay sequences; and concatenating at least two of said pairs of constituent Golay sequences to produce the extended sequence.
2. A method as claimed in claim 1 wherein the step of transforming the pair of constituent Golay sequences A and B to form each pair of transformed sequences comprises a permutation of elements of the sequences.
3. A method as claimed in claim 2 wherein said permutation comprises a reversal of the order of elements in the sequences.
4. A method as claimed in claim 2 or 3 wherein said permutation comprises a reversal of a set of address bits identifying locations of elements in the sequences.
5. A method as claimed is claim 2 or 3 wherein said permutation comprises a reversal of some but not all of a set of address bits identifying locations of elements in the sequences.
6. A method as claimed is any of claims 2 to 5 wherein sand permutation comprises a concatenation of subsets of elements of the sequences selected by decimation.
7. A method as claimed in claim 6 wherein there are two subsets of elements, in even and odd locations in the sequences, that are concatenated.
8. A method of producing a preamble for use on an access channel of a cellular communications system, wherein the preamble includes an extended sequence produced by the method of any of claims 1 to 7.
9. A method as claimed in claim 8 wherein each of the constituent Golay sequences A
and B and each of the transformed sequences comprises 256 elements, and the preamble comprises 4096 elements.
10. A method as claimed in claim 9 wherein the extended sequence comprises the constituent Golay sequences A and B and seven different transformations of these sequences A and B.

11. A method of providing a preamble for an access channel of a CDMA (code division multiple access) communications system, comprising the steps of:
providing a pair of constituent Golay sequences A and B;
permuting elements of the pair of sequences A and B to form at least one pair of transformed sequences which are also constituent Golay sequences; and concatenating said at least one pair of transformed sequences with the pair of constituent Golay sequences A and B for use as an extended sequence in the preamble.
12. A method us claimed in claim 11 wherein the preamble is provided by a concatenation of the pair of constituent Golay sequences A and B with a plurality of pairs of said transformed sequences according to different permutations of the elements of the pair of constituent Golay sequences A and B.
13. A method as claimed in claim 11 or 12 wherein the step of permuting elements of the pair of sequences A and B comprises a reversal of the order of elements in the sequences.
14. A method as claimed in any of claims 11 to 13 wherein the step of permuting elements of the pair of sequences A and B comprises a reversal of at least some of a set of address bits identifying locations of elements in the sequences.
15. A method as claimed is any of claims 11 to 13 wherein the step of permuting elements of the pair of sequences A and B comprises a concatenation of two subsets of elements of the sequences, the two subsets corresponding respectively to even and odd locations in the sequences.
15. Apparatus for use in carrying out the method of any of claims 1 to 15, comprising a memory for storing elements of each sequence, and address control means for addressing the memory for writing to or reading from the memory consecutively at locations according to the transformed sequences.
17. Apparatus as claimed in claim 16 wherein the address control means comprises a biditectional counter for supplying memory addresses incremented in either of two opposite directions, and an address permutation unit for permuting said addresses in accordance with the transformed sequences and for supplying the permuted addresses to the memory.

18. A preamble for an access channel of a CDMA (code division multiple access) communications system, comprising a pair of constituent Golay sequences A and B and, concatenated with the pair of constituent Golay sequences A and B, at least one pair of transformed sequences which are also constituent Golay sequences, each pair of transformed sequences comprising a permutation of elements of the pair of sequences A
any B.
19. A preamble as claimed in claim 18 comprising a plurality of pairs of said transformed sequences having different respective permutations of the elements of the pair of sequences A and H.
20. A preamble as claimed in claim 18 or 19 wherein a pair of said transformed sequences comprises the pair of sequence A and B with a reversed order of elements in the sequences.
21. A preamble as claimed in claim 18 or 19 wherein a pair of said transformed sequences comprises the pair of sequences A and B with elements is the sequences permuted in accordance with a reversed order of at least some of a set of address bits identifying locations of elements in the sequences.
22. A peramble as claimed in claim 18 or 19 wherein a pair of said transformed sequence comprises elements is even locations of the pair of sequences A and B
concatenated with elements in even locations in the pair of sequences A and B.